Skip to main content
SpringerLink
Log in

State-based buckling analysis of beam-like structures

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Beam, column, plate, and any other structure, under full or partial compressive loading, are prone to failure by the buckling phenomenon. At the instant of failure, the structure may be in unpredictable elastic, elastic–plastic, full plastic, cracked, or other forms of deterioration state. Therefore, in spite of so much study, there is no definite solution to the problem. In this paper a unified, simple, and exact theory is proposed where buckling is considered as the change of state of structure between intact and collapsed states, and then the buckling capacity is innovatively expressed via states and phenomena functions, which are explicitly defined as functions of state variable. The state variable is determined by calibration of the structure slenderness ratio. The efficacy of the work is verified via concise mathematical logics, and comparison of the results with those of the others via seven examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Euler, L.: Sur la force des colonnes. Mem. Acad. R. Sci. Belle Lett. 13, 309–318 (1759)

    Google Scholar 

  2. Pi, Y.L., Trahair, N.S.: Lateral distortional buckling of hollow flange beams. J. Struct. Eng. ASCE 123, 695–702 (1997)

    Article  Google Scholar 

  3. Kesti, J.: Local and distortional buckling of perforated steel wall studs. Ph.D. thesis, Department of Civil and Environmental Engineering, Helsinki University of Technology, Finland (2000)

  4. Wanniarachchi, S.: Flexural behavior and design of cold-formed steel beams with rectangular hollow flanges. Ph.D. thesis, School of Urban Developments, Queensland University of Technology, Australia (2005)

  5. Anapayan, T.: Flexural behavior and design of hollow flange steel beams. Ph.D. thesis, School of Urban Developments, Queensland University of Technology, Australia (2010)

  6. Kankanamge, N.D., Mahendran, M.: Behavior and design of cold formed steel beams subjected to lateral torsional buckling. Thin Walled Struct. 51(1), 25–38 (2012)

    Article  Google Scholar 

  7. Du, Y.: Lateral torsional buckling of wooden beam deck systems. M.Sc. thesis, Department of Civil Engineering, University of Ottawa, Canada (2016)

  8. Ranjbaran, A.: Analysis of cracked members: the governing equations and exact solutions. Iran. J. Sci. Technol. Trans. B Eng. 34(4), 407–417 (2010)

    MATH  Google Scholar 

  9. Ranjbaran, A., Rousta, H.: Interaction diagram for dynamic stability by Laplace transform. NED Univ. J. Res. 10(1), 31–38 (2013)

    Google Scholar 

  10. Ranjbaran, A., Rousta, H., Ranjbaran, M., Ranjbaran, M.: Dynamic stability of cracked columns; the stiffness reduction method. Sci. Iran. 20(1), 57–64 (2013)

    MATH  Google Scholar 

  11. Ranjbaran, A., Shokrzadeh, A.R., Khosravi, S.: A new finite element analysis of free axial vibration of cracked bars. Int. J. Numer. Methods Biomed. Eng. 27(10), 1611–1621 (2011)

    Article  MATH  Google Scholar 

  12. Ranjbaran, A., Rousta, H.: Finite element analysis of cracked beams innovative weak form equations. NED Univ. J. Res. 10(1), 39–46 (2013)

    Google Scholar 

  13. Ranjbaran, A., Rousta, H., Ranjbaran, M., Ranjbaran, M., Hashemi, M., Moravej, M.T.: A necessary modification for the finite element analysis of cracked members: detection, construction, and justification. Arch. Appl. Mech. 83(7), 1087–1096 (2013)

    Article  MATH  Google Scholar 

  14. Ranjbaran, A.: Square of the Dirac’s delta distribution: a new definition for engineering mechanics. NED Univ. J. Res. 11(1), 21–28 (2014)

    Google Scholar 

  15. Ranjbaran, A., Ranjbaran, M.: New finite-element formulation for buckling analysis of cracked structures. J. Eng. Mech. 140(5), 04014014(1–10) (2014). doi:10.1061/(ASCE)EM.1943-7889.0000734

    Article  Google Scholar 

  16. Ranjbaran, A.: Free-vibration analysis of stiffened frames. J. Eng. Mech. 140(9), 04014071(1–9) (2014). doi:10.1061/(ASCE)EM.1943-7889.0000783

    Article  Google Scholar 

  17. Ranjbaran, A.: New interpolation method for free vibration and stability analysis of cracked beams. NED Univ. J. Res. 12(3), 81–94 (2015)

    Google Scholar 

  18. Ranjbaran, A., Hashemi, M., Behnamianfar, F.: Dynamic stability analysis of functionally graded material beams. NED Univ. J. Res. 12(3), 95–106 (2015)

    Google Scholar 

  19. Ranjbaran, A.: Bench mark equations for determination of the main parameters of fracture mechanics. NED Univ. J. Res. 11(3), 29–38 (2014)

    Google Scholar 

  20. Ranjbaran, A., Ranjbaran, M.: State functions the milestone of fracture. Arch. Appl. Mech. 86(7), 1311–1324 (2016). doi:10.1007/s00419-015-1115-3

    Article  Google Scholar 

  21. Kankanamge, N.D.: Behaviour and design of cold-formed steel beams at elevated temperatures. Ph.D. thesis, School of Urban Developments, Queensland University of Technology, Australia (2010)

  22. AISC.: Load and resistance factor design specification, for structural steel buildings. American Institute of Steel Construction, Inc., Chicago (1999)

  23. Kankanamge, N.D., Mahendran, M.: Mechanical properties of cold-formed steels at elevated temperature. Thin Walled Struct. 49(1), 26–44 (2011)

    Article  Google Scholar 

  24. Kankanamge, N.D., Mahendran, M.: Behaviour and design of cold-formed steel beams subject to lateral-torsional buckling at elevated temperature. Thin Walled Struct. 61, 213–228 (2012)

    Article  Google Scholar 

  25. Verweij, J.G.: Cellular beam-columns in portal frame structures. M.Sc. thesis, Department of Civil Engineering, Delft University of Technology, Netherlands (2010)

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Shiraz University, Shiraz, 71348 51156, Iran

    Abdolrasoul Ranjbaran

  2. Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Ranjbaran

Authors
  1. Abdolrasoul Ranjbaran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Ranjbaran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdolrasoul Ranjbaran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ranjbaran, A., Ranjbaran, M. State-based buckling analysis of beam-like structures. Arch Appl Mech 87, 1555–1565 (2017). https://doi.org/10.1007/s00419-017-1273-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-017-1273-6

Keywords

Search

Navigation